Question

Angle b = 61, angle c = 57, and angle A = 2x. What does x equal when triangle ACB is congruent to triangle DCE?

a. 20
b. 25
c. 30
d. 35

Answer 1

To find x in the congruent triangles ACB and DCE, we set up an equation using corresponding angles and solve for x.

Step-by-step explanation:

Given that triangle ACB is congruent to triangle DCE, we can use the corresponding angles property to find the value of x. By comparing angles, we have: angle C = angle E = 57 and angle A = angle D = 2x. Also, angle B = angle C = 61.

Since the sum of angles in a triangle is always 180 degrees, we can set up the equation: angle A + angle B + angle C = 180. Substituting in the values, we get: 2x + 61 + 57 = 180.

Simplifying the equation, we have: 2x + 118 = 180. Subtracting 118 from both sides, we get: 2x = 62. Dividing both sides by 2, we find that x = 31.